O(mlogn)O(mlogn) split decomposition of strongly-connected graphs

In the early 1980s, Cunningham described a unique decomposition of a strongly-connected graph. A linear time bound for finding it in the special case of an undirected graph has been given previously, but up until now, the best bound known for the general case has been O(n3)O(n3). We give an O(mlogn)O(mlogn) bound.